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Simplifying (X + -1(-2 + -4i))(x + -1(-2 + 4i)) = 0 (X + (-2 * -1 + -4i * -1))(x + -1(-2 + 4i)) = 0 (X + (2 + 4i))(x + -1(-2 + 4i)) = 0 Reorder the terms: (2 + X + 4i)(x + -1(-2 + 4i)) = 0 (2 + X + 4i)(x + (-2 * -1 + 4i * -1)) = 0 (2 + X + 4i)(x + (2 + -4i)) = 0 Reorder the terms: (2 + X + 4i)(2 + -4i + x) = 0 Multiply (2 + X + 4i) * (2 + -4i + x) (2(2 + -4i + x) + X(2 + -4i + x) + 4i * (2 + -4i + x)) = 0 ((2 * 2 + -4i * 2 + x * 2) + X(2 + -4i + x) + 4i * (2 + -4i + x)) = 0 ((4 + -8i + 2x) + X(2 + -4i + x) + 4i * (2 + -4i + x)) = 0 (4 + -8i + 2x + (2 * X + -4i * X + x * X) + 4i * (2 + -4i + x)) = 0 (4 + -8i + 2x + (2X + -4iX + xX) + 4i * (2 + -4i + x)) = 0 (4 + -8i + 2x + 2X + -4iX + xX + (2 * 4i + -4i * 4i + x * 4i)) = 0 Reorder the terms: (4 + -8i + 2x + 2X + -4iX + xX + (8i + 4ix + -16i2)) = 0 (4 + -8i + 2x + 2X + -4iX + xX + (8i + 4ix + -16i2)) = 0 Reorder the terms: (4 + 2X + -8i + 8i + -4iX + 4ix + -16i2 + 2x + xX) = 0 Combine like terms: -8i + 8i = 0 (4 + 2X + 0 + -4iX + 4ix + -16i2 + 2x + xX) = 0 (4 + 2X + -4iX + 4ix + -16i2 + 2x + xX) = 0 Solving 4 + 2X + -4iX + 4ix + -16i2 + 2x + xX = 0 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + 2X + -4iX + 4ix + -16i2 + 2x + -4 + xX = 0 + -4 Reorder the terms: 4 + -4 + 2X + -4iX + 4ix + -16i2 + 2x + xX = 0 + -4 Combine like terms: 4 + -4 = 0 0 + 2X + -4iX + 4ix + -16i2 + 2x + xX = 0 + -4 2X + -4iX + 4ix + -16i2 + 2x + xX = 0 + -4 Combine like terms: 0 + -4 = -4 2X + -4iX + 4ix + -16i2 + 2x + xX = -4 Add '-4ix' to each side of the equation. 2X + -4iX + 4ix + -16i2 + 2x + -4ix + xX = -4 + -4ix Reorder the terms: 2X + -4iX + 4ix + -4ix + -16i2 + 2x + xX = -4 + -4ix Combine like terms: 4ix + -4ix = 0 2X + -4iX + 0 + -16i2 + 2x + xX = -4 + -4ix 2X + -4iX + -16i2 + 2x + xX = -4 + -4ix Add '16i2' to each side of the equation. 2X + -4iX + -16i2 + 2x + 16i2 + xX = -4 + -4ix + 16i2 Reorder the terms: 2X + -4iX + -16i2 + 16i2 + 2x + xX = -4 + -4ix + 16i2 Combine like terms: -16i2 + 16i2 = 0 2X + -4iX + 0 + 2x + xX = -4 + -4ix + 16i2 2X + -4iX + 2x + xX = -4 + -4ix + 16i2 Add '-2x' to each side of the equation. 2X + -4iX + 2x + -2x + xX = -4 + -4ix + 16i2 + -2x Combine like terms: 2x + -2x = 0 2X + -4iX + 0 + xX = -4 + -4ix + 16i2 + -2x 2X + -4iX + xX = -4 + -4ix + 16i2 + -2x Reorder the terms: 4 + 2X + -4iX + 4ix + -16i2 + 2x + xX = -4 + -4ix + 16i2 + -2x + 4 + 4ix + -16i2 + 2x Reorder the terms: 4 + 2X + -4iX + 4ix + -16i2 + 2x + xX = -4 + 4 + -4ix + 4ix + 16i2 + -16i2 + -2x + 2x Combine like terms: -4 + 4 = 0 4 + 2X + -4iX + 4ix + -16i2 + 2x + xX = 0 + -4ix + 4ix + 16i2 + -16i2 + -2x + 2x 4 + 2X + -4iX + 4ix + -16i2 + 2x + xX = -4ix + 4ix + 16i2 + -16i2 + -2x + 2x Combine like terms: -4ix + 4ix = 0 4 + 2X + -4iX + 4ix + -16i2 + 2x + xX = 0 + 16i2 + -16i2 + -2x + 2x 4 + 2X + -4iX + 4ix + -16i2 + 2x + xX = 16i2 + -16i2 + -2x + 2x Combine like terms: 16i2 + -16i2 = 0 4 + 2X + -4iX + 4ix + -16i2 + 2x + xX = 0 + -2x + 2x 4 + 2X + -4iX + 4ix + -16i2 + 2x + xX = -2x + 2x Combine like terms: -2x + 2x = 0 4 + 2X + -4iX + 4ix + -16i2 + 2x + xX = 0 The solution to this equation could not be determined.
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